tutoR

David J. Harris
December 6-7, 2014

Workshop goals:

  • Learn enough to get started on your own
  • Learn what tools are available for when you need them

  • Don't try to absorb everything.

    Ask lots of questions!

Topics

  • Saturday morning
    • Introduction, examples
    • Talking to R
    • Getting help
    • Errors, warnings, & bugs
    • Data
  • Saturday afternoon
    • Plotting
    • Importing data
    • Loops
    • Stats
  • Sunday
    • text
    • functions
    • formatting excel data
    • reproducibility

Why code?

  • Automation
  • Reproducibility
  • Customization

Example 1: data cleaning

library(taxize)
tnrs(query = mynames, source = "iPlant_TNRS")[ , c(1:2)]

        submittedname        acceptedname
7   Helianthus annuus   Helianthus annuus
4       Pinus contort      Pinus contorta
5            Poa anua           Poa annua
3      Abis magnifica     Abies magnifica
8     Rosa california    Rosa californica
2  Festuca arundinace Festuca arundinacea
1 Sorbus occidentalos Sorbus occidentalis
6        Madia sateva        Madia sativa

Example 2: Data cleaning

34.868688 N, 87.6041417 W 
34.6386747 N, 87.1912919 W 
34.8 N, 87.7333333 W 
34.0297881 N, 87.0592352 W 
34.2016687 N, 86.4934089 W 
34.5012877 N, 86.6855493 W 

# Throw out everything from the first space to the end
north = as.numeric(gsub(" .*$", "", latlon))

# Retain only the bit between ", " and " W"
west = -as.numeric(gsub(".*, (.*) W", "\\1", z))

Example 2: Mapping bird distributions

(see “bbs.html”)

Questions?

Why R?

It's what your colleagues use

  • packages to do stuff you want
  • interfaces with everything else
  • share code with colleagues

RStudio

Questions?

Talking to R

R is like your old graphing calculator

Arithemetic works like you'd expect:

(1 + 1 * 3)^3

[1] 64

So do lots of basic math functions:

cos(pi)

[1] -1

R is like your old graphing calculator

R can also make graphs

plot(function(x) sin(x^2), from = 0, to = 5)

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Code can include "comments"

Anything following “#” is ignored through the end of the line.

1+1 # This is a comment.  R ignores it.

[1] 2

2+2 # But tomorrow, it could be helpful

[1] 4

# for understanding the code you
# wrote today.

Questions?

Assignment: Data can have names

Referring back to our data

  • Don't always want to type 525600 for number of minutes in a year.
  • Want to separate data from code:
    • Insect biomass = fly biomass + beetle biomass + bug biomass
    • Total biomass = fly biomass + beetle biomass + bug biomass + algae biomass
  • Only need to update fly biomass once.

Giving a name to your data

  • name <- data             or             name = data
    • “The container called 'name' gets filled with the data”
insect_biomass = 12
area = 50
proportion_ants = .3

insect_biomass / area

[1] 0.24

insect_biomass * proportion_ants

[1] 3.6

Questions?

Changing saved values

x = 2  # Save "2"" with the name "x"
y = x  # save x's current value with the name "y"

x = 3  # Change x's value to 3
x

[1] 3
  • What's y's value?
y

[1] 2

Keeping track of what you've saved

  • RStudio tells you what you've saved in the upper-right under “Environment→Global Environment”
  • Sometimes also called the “workspace”
  • Can also access it with the ls() or objects commands
  • Clear everything out with the broom icon

Using functions

Using functions:

(sin(1) + log(5)) / 3

[1] 0.817

Functions are verbs

“Take this thing and do the function to it”

  • Take this cookie and eat it
  • Take this number and square it
cos(pi) # Take pi and *calculate its cosine*

[1] -1

log(area) # Take `area` & *calculate its log*

[1] 3.912

Functions can have modifiers

  • Take this cookie and eat it carefully
log(area, base = 2) # Take `area` & *calculate its log* *in base 2*

[1] 5.644

rep(5, times = 7) # Take 5 and *repeat* it 7 times*

[1] 5 5 5 5 5 5 5
  • Data & modifiers passed to functions are called arguments

Anatomy of a function call

  • Name of function (sin, log, rep)
  • Parentheses enclosing the arguments
  • Arguments, separated by commas

Arguments

Naming the arguments is (usually) optional:

log(3, 2)

[1] 1.585

log(x = 3, base = 2)

[1] 1.585

Some arguments have default values that don't need to be specified: these can be found on the help pages.

Questions so far?

There are tons of functions!

  • You don't need to know all of them
  • Most common R usage pattern: use pre-written functions on your custom data
    • do standard actions to your unique stuff
  • You can also write your own functions

<Break>

Getting help

Help files

  • ?function_name or help(function_name)
help(rep)
?rep
  • Some special functions like “+” need to be quoted; quoting never hurts

Parts of a help file

  • Title: big picture in big text
  • Description: summary
  • Usage: very minimal examples
  • Arguments: list of ways you can customize the function's action for your needs
  • Details: Details
  • Value: What you get out of the function
  • Examples (consider starting here): ways to use the function

Some help files have a Note or Warning section for even more information

Help files are annoying

  • Need to know the function name
  • Operators and special things need backticks
  • Written for programmers, by programmers
  • Might need to look in 3-4 different sections.
    • Jump around, focus on Usage and Examples
  • It gets easier

Other help sources (part 1)

Other help sources (part 2)

  • Google, http://www.rseek.org/
    • Stack Overflow / Cross Validated (read and/or ask)
    • R-help lists (read-only!)
  • Davis R Users Group (and mailing list: read and/or ask)
  • More tips

Other help sources (part 2)

Getting ahead of the curve

Books/courses

R “Gotcha's”

Questions?

When things go wrong

  • Errors
    • “Something went so badly wrong that I stopped and gave up before I broke something”
    • 1 + "two"
Error in 1 + "two" : non-numeric argument to binary operator
  • Warnings
    • “Something might be wrong, but I kept going”
    • log(-1)
[1] NaN
Warning message:
In log(-1) : NaNs produced

When things go wrong

  • Bugs:
    • “I told R to do the wrong thing”
    • These are the scariest, because you don't always know your code is wrong.
  • More on errors and warnings

A horrifying bug

pi = 7
#
# 100 lines of code later...
#
cos(pi)

[1] 0.7539

Questions?

Break

Data (nouns)

Vectors

We've already seen scalars

area = 50
  • Data can also form vectors
rep(1, times = 5)

[1] 1 1 1 1 1

Making your own vectors

Use the c (“combine”) function

  • Elements have a position and (optionally) names
biomass = c(bugs = 12.1, flies = 23.7, beetles = 3.1)
biomass2 = c(bugs = 7.1, flies = 3.8, beetles = 8.2)
  • Concatenate vectors with c as well.
both_biomass = c(biomass, biomass2)

Vectors can hold different kinds of data

  • Vectors always belong to one “type”
    • logical: TRUE or FALSE
    • integer: …, -1, 0, 1, 2, …
    • numeric: 3.141592653589793115998, 2.718281828459045090796
    • character: “anything”, “3”, “ΣΔΘ™”
  • R “promotes” vectors when concatenated:
    • c(biomass, "not a number") is a character vector

Questions?

Arithmetic on vectors:

Arithmetic works element-by-element (based on position, not name!)

biomass

   bugs   flies beetles 
   12.1    23.7     3.1 

biomass2

   bugs   flies beetles 
    7.1     3.8     8.2 

biomass + biomass2

   bugs   flies beetles 
   19.2    27.5    11.3

Shorter vectors are "recycled"

biomass

   bugs   flies beetles 
   12.1    23.7     3.1 

area

[1] 50

biomass / area

   bugs   flies beetles 
  0.242   0.474   0.062

Recycling can be dangerous!

c(10, 20) + c(1, 2, 3, 4)

[1] 11 22 13 24

You can also compare vectors

Greater-than-or-equal (≥, typed as >=)

biomass >= biomass2

   bugs   flies beetles 
   TRUE    TRUE   FALSE

Test for equality with ==

5 == 5 * 1

[1] TRUE
  • Be careful about rounding error!
(1.0 - 0.9 - 0.1) == 0

[1] FALSE

  • \( 1.0 - 0.9 - 0.1 = -2.78^{-17} \)

  • use all.equal instead

Getting data out of a vector with [square brackets]

We want the second element of our vector, which has fly biomass

   bugs   flies beetles 
   12.1    23.7     3.1 

biomass["flies"]               # By name
biomass[2]                     # By index
biomass[c(-1, -3)]             # Drop negatives
biomass[c(FALSE, TRUE, FALSE)] # With logic
biomass[biomass > 20]          # With a test

Factors

  • Describes categories like experimental treatments
    • “Nitrogen addition”, “Phosphorous addition”, “Control”
factor(c("Nitrogen addition", "Phosphorous addition",  "Control", "Nitrogen addition"))

Stored internally as 1, 2, 3!

Questions about vectors?

Data frames

Remember biomass and biomass2?

  • What if you have biomasses at 100 sites?
biomass_df = data.frame(
  site = c("site 1", "site 2", "site 3", "site 4", "site 5"), 
  bugs = c(12.1, 7.1, 2.8, 12.5, 3.1), 
  flies = c(23.7, 3.8, 11.3, 32.1, 11.9),
  beetles = c(3.1, 8.2, 17.1, 3.9, 11.7)
)

Data frames

biomass_df = data.frame(
  site = c("site 1", "site 2", "site 3", "site 4", "site 5"), 
  bugs = c(12.1, 7.1, 2.8, 12.5, 3.1), 
  flies = c(23.7, 3.8, 11.3, 32.1, 11.9),
  beetles = c(3.1, 8.2, 17.1, 3.9, 11.7)
)

A data.frame has one column for each variable, and one row for each replicate.

Each variable is a vector.

Variables can be different types

Can contain missing values (NA)

Learning about your objects

# Structure of object
str(biomass_df) # Rstudio has same info

'data.frame':   5 obs. of  4 variables:
 $ site   : Factor w/ 5 levels "site 1","site 2",..: 1 2 3 4 5
 $ bugs   : num  12.1 7.1 2.8 12.5 3.1
 $ flies  : num  23.7 3.8 11.3 32.1 11.9
 $ beetles: num  3.1 8.2 17.1 3.9 11.7

# Top 6 rows.with "head"
head(InsectSprays) # "Tail" gives bottom 6

  count spray
1    10     A
2     7     A
3    20     A
4    14     A
5    14     A
6    12     A

Learning about your objects

class(biomass_df)  # What is it?

[1] "data.frame"

length(biomass_df) # Number of vectors in DF

[1] 4

dim(biomass_df)    # Dimensions

[1] 5 4

plot(biomass_df)   # What's it look like?

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Subsetting data frames

biomass_df$flies # pull out fly vector

[1] 23.7  3.8 11.3 32.1 11.9

# rows 1 and 2, columns "flies" and "beetles"
biomass_df[c(1, 2), c("flies", "beetles")]

  flies beetles
1  23.7     3.1
2   3.8     8.2

Subsetting data frames

  • [ versus [[ versus $
    • $ works on lists (including data frames). Pulls out one element (e.g. a vector)
    • [[ works on anything: pulls out one element (e.g. a vector)
    • [ works on anything: pulls out one or more elements, leaving them in their original container (e.g. a dataframe).

Questions?

Lunch!

Plotting

Workhorse is the plot function

plot(biomass_df)

plot of chunk unnamed-chunk-44

Plotting

Workhorse is the plot function

# The tilde indicates a "formula"
# "data" tells R where to look for flies/bugs
plot(flies ~ bugs , data = biomass_df)

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Plotting

Workhorse is the plot function

plot(function(x) sin(x^2), from = 0, to = 5)

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Plotting

Lots of other functions too!

hist(biomass_df$beetles)

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A blank canvas

plot(NULL, xlim = range(biomass_df$bugs), ylim = range(biomass_df$flies), xlab = "bug biomass (g/m^2)", ylab = "fly biomass (g/m^2)")

plot of chunk unnamed-chunk-48

Adding points to the canvas

points(bugs ~ flies , data = biomass_df)

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Spicing it up

arrows(x0 = 5, y0=8, x1 = 12, y1 = 20, lwd = 5, col = "blue")
text(x = 5, y = 20, labels = "Text", cex = 3)

plot of chunk unnamed-chunk-52

Questions?

Customization alphabet soup

?par

  • main: main plot title
  • sub: plot subtitle
  • xlab/ylab: axis labels,
  • log: which axes should be on log scale
  • type: line, point, both, etc.
  • cex: character expansion (size factor)
  • mfrow/mfcol: Number of rows & columns on canvas
  • pch: plotting character
  • col: color
  • lty: line type (dashed, dotted, etc)
  • lwd: line width
  • bty: box type
  • mgp: margin size
  • axes: TRUE/FALSE
  • asp: Aspect ratio

A real example

A real example

par(mfrow = c(2, 1)) # 2 rows of plots

myyellow = rgb(red = 1, green = 1, blue = 0, alpha = .4)

# Plot the first beaver's temp versus time
plot(temp ~ time, data = beaver1, main = "Beaver 1")

# Giant rectangle
rect(xleft = 800, xright = 1500, ytop = 1000, ybottom = -1000, col = myyellow, border = NA)

# Plot 2nd beaver's temperature versus time
plot(temp ~ time, data = beaver2, main = "Beaver 2")
rect(xleft = 800, xright = 1500, ytop = 1000, ybottom = -1000, col = myyellow, border = NA)

A real example

plot of chunk unnamed-chunk-55

A real example

A real example

A real example

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Saving your plots

  • Rstudio “Export” button
  • Other graphics devices (png, pdf, jpeg, tiff, etc.)
# Set up the plotting device
pdf("figures/myplot.pdf", length = 7, width = 5)

# As many lines of graphics code as you'd like
plot(count ~ spray, data = InsectSprays)

# Seal up the pdf
dev.off()

Maps

library(mapdata)
# Tweak the margins
par("mai" = c(0, 0, 0, 0))
map(
  database = "worldHires", 
  proj = "albers", 
  param = c(29.5, 45.5),
  interior = TRUE,
  ylim = c(25, 75),
  xlim = c(-167, -53),
  resolution = 0.1,
  wrap = TRUE,
  col = "gray",
  mar = c(0, 0, 0, 0),
  myborder = 0,
  orientation = c(95, -102, 0),
  lwd = 2
)

Maps

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Other graphics systems: ggplot2

 qplot(x = displ, y = hwy, data = mpg, color = drv) + facet_wrap(~ cyl)

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Other graphics systems: Lattice

xyplot(hwy ~ displ | cyl, data = mpg, groups = drv)

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Importing data

Spreadsheets

  • read.csv(file = "filename.csv")
    • stringsAsFactors=FALSE
    • header?
    • data.table::fread is often faster
head(read.csv("routes.csv")[3:6], header = TRUE, stringsAsFactors = FALSE)

  Route Active  Lati  Longi
1     1      1 34.87 -87.60
2     2      0 34.64 -87.19
3     3      0 34.80 -87.73
4     4      1 34.03 -87.06
5     5      0 34.20 -86.49
6     6      1 34.50 -86.69

Excel and databases

Spatial data

  • Methods for importing shapefiles
  • The raster package is very efficient with large raster
  • The sp package has a lot of low-level spatial machinery (e.g. projections)
  • maps, mapdata, and maptools for drawing maps in base graphics
  • RgoogleMaps talks to Google Maps
  • ggmap does maps in ggplot2
  • Spatial task view

Talking to the Internet

  • twitteR package

Loops and automation

Computers are good at repetition

rep("computers are good at repetition", 1000)

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 [836] "computers are good at repetition"
 [837] "computers are good at repetition"
 [838] "computers are good at repetition"
 [839] "computers are good at repetition"
 [840] "computers are good at repetition"
 [841] "computers are good at repetition"
 [842] "computers are good at repetition"
 [843] "computers are good at repetition"
 [844] "computers are good at repetition"
 [845] "computers are good at repetition"
 [846] "computers are good at repetition"
 [847] "computers are good at repetition"
 [848] "computers are good at repetition"
 [849] "computers are good at repetition"
 [850] "computers are good at repetition"
 [851] "computers are good at repetition"
 [852] "computers are good at repetition"
 [853] "computers are good at repetition"
 [854] "computers are good at repetition"
 [855] "computers are good at repetition"
 [856] "computers are good at repetition"
 [857] "computers are good at repetition"
 [858] "computers are good at repetition"
 [859] "computers are good at repetition"
 [860] "computers are good at repetition"
 [861] "computers are good at repetition"
 [862] "computers are good at repetition"
 [863] "computers are good at repetition"
 [864] "computers are good at repetition"
 [865] "computers are good at repetition"
 [866] "computers are good at repetition"
 [867] "computers are good at repetition"
 [868] "computers are good at repetition"
 [869] "computers are good at repetition"
 [870] "computers are good at repetition"
 [871] "computers are good at repetition"
 [872] "computers are good at repetition"
 [873] "computers are good at repetition"
 [874] "computers are good at repetition"
 [875] "computers are good at repetition"
 [876] "computers are good at repetition"
 [877] "computers are good at repetition"
 [878] "computers are good at repetition"
 [879] "computers are good at repetition"
 [880] "computers are good at repetition"
 [881] "computers are good at repetition"
 [882] "computers are good at repetition"
 [883] "computers are good at repetition"
 [884] "computers are good at repetition"
 [885] "computers are good at repetition"
 [886] "computers are good at repetition"
 [887] "computers are good at repetition"
 [888] "computers are good at repetition"
 [889] "computers are good at repetition"
 [890] "computers are good at repetition"
 [891] "computers are good at repetition"
 [892] "computers are good at repetition"
 [893] "computers are good at repetition"
 [894] "computers are good at repetition"
 [895] "computers are good at repetition"
 [896] "computers are good at repetition"
 [897] "computers are good at repetition"
 [898] "computers are good at repetition"
 [899] "computers are good at repetition"
 [900] "computers are good at repetition"
 [901] "computers are good at repetition"
 [902] "computers are good at repetition"
 [903] "computers are good at repetition"
 [904] "computers are good at repetition"
 [905] "computers are good at repetition"
 [906] "computers are good at repetition"
 [907] "computers are good at repetition"
 [908] "computers are good at repetition"
 [909] "computers are good at repetition"
 [910] "computers are good at repetition"
 [911] "computers are good at repetition"
 [912] "computers are good at repetition"
 [913] "computers are good at repetition"
 [914] "computers are good at repetition"
 [915] "computers are good at repetition"
 [916] "computers are good at repetition"
 [917] "computers are good at repetition"
 [918] "computers are good at repetition"
 [919] "computers are good at repetition"
 [920] "computers are good at repetition"
 [921] "computers are good at repetition"
 [922] "computers are good at repetition"
 [923] "computers are good at repetition"
 [924] "computers are good at repetition"
 [925] "computers are good at repetition"
 [926] "computers are good at repetition"
 [927] "computers are good at repetition"
 [928] "computers are good at repetition"
 [929] "computers are good at repetition"
 [930] "computers are good at repetition"
 [931] "computers are good at repetition"
 [932] "computers are good at repetition"
 [933] "computers are good at repetition"
 [934] "computers are good at repetition"
 [935] "computers are good at repetition"
 [936] "computers are good at repetition"
 [937] "computers are good at repetition"
 [938] "computers are good at repetition"
 [939] "computers are good at repetition"
 [940] "computers are good at repetition"
 [941] "computers are good at repetition"
 [942] "computers are good at repetition"
 [943] "computers are good at repetition"
 [944] "computers are good at repetition"
 [945] "computers are good at repetition"
 [946] "computers are good at repetition"
 [947] "computers are good at repetition"
 [948] "computers are good at repetition"
 [949] "computers are good at repetition"
 [950] "computers are good at repetition"
 [951] "computers are good at repetition"
 [952] "computers are good at repetition"
 [953] "computers are good at repetition"
 [954] "computers are good at repetition"
 [955] "computers are good at repetition"
 [956] "computers are good at repetition"
 [957] "computers are good at repetition"
 [958] "computers are good at repetition"
 [959] "computers are good at repetition"
 [960] "computers are good at repetition"
 [961] "computers are good at repetition"
 [962] "computers are good at repetition"
 [963] "computers are good at repetition"
 [964] "computers are good at repetition"
 [965] "computers are good at repetition"
 [966] "computers are good at repetition"
 [967] "computers are good at repetition"
 [968] "computers are good at repetition"
 [969] "computers are good at repetition"
 [970] "computers are good at repetition"
 [971] "computers are good at repetition"
 [972] "computers are good at repetition"
 [973] "computers are good at repetition"
 [974] "computers are good at repetition"
 [975] "computers are good at repetition"
 [976] "computers are good at repetition"
 [977] "computers are good at repetition"
 [978] "computers are good at repetition"
 [979] "computers are good at repetition"
 [980] "computers are good at repetition"
 [981] "computers are good at repetition"
 [982] "computers are good at repetition"
 [983] "computers are good at repetition"
 [984] "computers are good at repetition"
 [985] "computers are good at repetition"
 [986] "computers are good at repetition"
 [987] "computers are good at repetition"
 [988] "computers are good at repetition"
 [989] "computers are good at repetition"
 [990] "computers are good at repetition"
 [991] "computers are good at repetition"
 [992] "computers are good at repetition"
 [993] "computers are good at repetition"
 [994] "computers are good at repetition"
 [995] "computers are good at repetition"
 [996] "computers are good at repetition"
 [997] "computers are good at repetition"
 [998] "computers are good at repetition"
 [999] "computers are good at repetition"
[1000] "computers are good at repetition"

Humans are bad at repetition

Humans are bad at repetition

species = "grouse"
#
# 100 lines of code...
#
species = "turkey"
#
# 100 lines of identical code...
#
species = "prairie chicken"
#
# 100 lines of identical code...
#

While

As long as some condition holds, keep doing stuff in braces.

while(1 > 0){
  print("Dave is cool!!!!!!!!")
}

[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
[1] "Dave is cool!!!!!!!!"
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[1] "Dave is cool!!!!!!!!"
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replicate

results = replicate(
  1000,
  mean(rnorm(10)) # Average of 10 standard normals
)

sd(results) # Should be about sqrt(1/10)

[1] 0.3189

While

As long as some condition holds, keep doing stuff in braces.

result = 2           # Start at 2
done = FALSE         # Task starts incomplete

while(!done){
  result = result^2 # Update result
  print(result)     # display result

  # See if we're done
  if(result > 100){done = TRUE}
}

[1] 4
[1] 16
[1] 256

For

Do something for each element of x

for(species in c("frog", "penguin", "rat")){
  new_name = paste0(toupper(species), "!")
  print(new_name)
}

[1] "FROG!"
[1] "PENGUIN!"
[1] "RAT!"

For

Do something for each element of x

for(species in unique(finch$Aou)){
  # Make one of these plots
}

*apply

S-apply (simplified-apply) does something to each element of your data set and returns a simplified result (e.g. a vector or matrix)

sapply(biomass_df, mean)

   site    bugs   flies beetles 
     NA    7.52   16.56    8.80

Vector operations are faster than loops

x = rnorm(10000)
system.time(x + 1)

   user  system elapsed 
      0       0       0 

x_plus_one = numeric(length(x))
system.time(
  for(i in seq_along(x)){
    x_plus_one[i] = x[i] + 1
  }
)

   user  system elapsed 
  0.013   0.001   0.013

Questions?

Statistics

t-test

?t.test

t.test(x = c(1, 2, 3, 1, 8, 5, 3), y = NULL, alternative = "two.sided", mu = 0, paired = FALSE, conf.level = 0.95)


    One Sample t-test

data:  c(1, 2, 3, 1, 8, 5, 3)
t = 3.481, df = 6, p-value = 0.01313
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 0.9758 5.5956
sample estimates:
mean of x 
    3.286

t-test: contents of the result

str(t.test(x = c(1, 2, 3, 1, 8, 5, 3)))

List of 9
 $ statistic  : Named num 3.48
  ..- attr(*, "names")= chr "t"
 $ parameter  : Named num 6
  ..- attr(*, "names")= chr "df"
 $ p.value    : num 0.0131
 $ conf.int   : atomic [1:2] 0.976 5.596
  ..- attr(*, "conf.level")= num 0.95
 $ estimate   : Named num 3.29
  ..- attr(*, "names")= chr "mean of x"
 $ null.value : Named num 0
  ..- attr(*, "names")= chr "mean"
 $ alternative: chr "two.sided"
 $ method     : chr "One Sample t-test"
 $ data.name  : chr "c(1, 2, 3, 1, 8, 5, 3)"
 - attr(*, "class")= chr "htest"

t-test: extracting results

t.test(x = c(1, 2, 3, 1, 8, 5, 3))$p.value

[1] 0.01313

t.test(x = c(1, 2, 3, 1, 8, 5, 3))$conf.int

[1] 0.9758 5.5956
attr(,"conf.level")
[1] 0.95

Chi-square test

chisq.test(c(11, 15), p = c(.25, .75))


    Chi-squared test for given probabilities

data:  c(11, 15)
X-squared = 4.154, df = 1, p-value = 0.04154

linear model

plot(count ~ spray, data = InsectSprays)

plot of chunk unnamed-chunk-80

linear model

lm(count ~ spray, data = InsectSprays)


Call:
lm(formula = count ~ spray, data = InsectSprays)

Coefficients:
(Intercept)       sprayB       sprayC       sprayD       sprayE  
     14.500        0.833      -12.417       -9.583      -11.000  
     sprayF  
      2.167

linear model

summary(lm(count ~ spray, data = InsectSprays))


Call:
lm(formula = count ~ spray, data = InsectSprays)

Residuals:
   Min     1Q Median     3Q    Max 
 -8.33  -1.96  -0.50   1.67   9.33 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   14.500      1.132   12.81  < 2e-16 ***
sprayB         0.833      1.601    0.52     0.60    
sprayC       -12.417      1.601   -7.76  7.3e-11 ***
sprayD        -9.583      1.601   -5.99  9.8e-08 ***
sprayE       -11.000      1.601   -6.87  2.8e-09 ***
sprayF         2.167      1.601    1.35     0.18    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.92 on 66 degrees of freedom
Multiple R-squared:  0.724, Adjusted R-squared:  0.704 
F-statistic: 34.7 on 5 and 66 DF,  p-value: <2e-16

linear model

anova(lm(count ~ spray, data = InsectSprays))

Analysis of Variance Table

Response: count
          Df Sum Sq Mean Sq F value Pr(>F)    
spray      5   2669     534    34.7 <2e-16 ***
Residuals 66   1015      15                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Model formulas

?formula

  • Formulas are not normal R code
  • Variables included in the model are separated by “+”
  • a * b means to include a, b, and their interaction
  • Can “inhibit” formula interpretation with the I function

Generalized linear models

summary(glm(count ~ spray, data = InsectSprays, family = poisson))


Call:
glm(formula = count ~ spray, family = poisson, data = InsectSprays)

Deviance Residuals: 
   Min      1Q  Median      3Q     Max  
-2.385  -0.888  -0.148   0.606   2.692  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept)   2.6741     0.0758   35.27   <2e-16 ***
sprayB        0.0559     0.1057    0.53     0.60    
sprayC       -1.9402     0.2139   -9.07   <2e-16 ***
sprayD       -1.0815     0.1507   -7.18    7e-13 ***
sprayE       -1.4214     0.1719   -8.27   <2e-16 ***
sprayF        0.1393     0.1037    1.34     0.18    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 409.041  on 71  degrees of freedom
Residual deviance:  98.329  on 66  degrees of freedom
AIC: 376.6

Number of Fisher Scoring iterations: 5

Mixed effects

  • lme4 package, lmer and glmer functions
  • use “|” (above the “enter” key) to mark random effects

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